'+pages+''); $('.stream > div:odd').addClass('bgr_color'); updateHeight('#history'); }); window.activateTabArea = ensure(function(tab, areas){ var parsed = false; var parts = (areas || '').split('/'); window.fsonload = $.inArray('fs', parts) >= 0; if(fsonload){ parts.splice(parts.indexOf('fs'), 1); } var replayMode = false; if($.inArray('replay', parts)>=0){ replayMode = 'replay'; } var noSoundMode = false; if($.inArray('nosound', parts)>=0){ noSoundMode = 'nosound'; } if($.inArray('ns', parts)>=0){ noSoundMode = 'ns'; } var previewMode = null; if($.inArray('p', parts)>=0){ previewMode = 'p'; } if($.inArray('preview', parts)>=0){ previewMode = 'preview'; } if($.inArray('repeat', parts)>=0){ replayMode = 'repeat'; } if($.inArray('r', parts)>=0 || $.inArray('ro', parts)>=0){ replayMode = 'r'; } if(replayMode){ parts.splice(parts.indexOf(replayMode), 1); } if(noSoundMode){ parts.splice(parts.indexOf(noSoundMode), 1); } if(previewMode){ parts.splice(parts.indexOf(previewMode), 1); } if(previewMode){ if(!parts.length){ parts = ['1-14', '999:59']; } } var area = parts[0]; if(tab == 'history' && false){ var page = parseInt(area || '1') || 1; $.ajax({ url: 'https://login.wn.com/recent/json/?pp='+history_pp+'&skip='+history_pp*(page-1), dataType: 'jsonp', success: function(response){ $ensure(function(){ renderHistory(response, page); }); } }); return true; } if(tab == 'global_history' && false){ var page = parseInt(area || '1') || 1; globalHistory.fetchStream(page, '', function(){ updateHeight('#global_history'); }); return true; } if(tab == 'my_playlists' && false){ var page = parseInt(area || '1') || 1; myPlaylists.fetchStream(page, '', function(){ updateHeight('#my_playlists'); }); return true; } if(tab == 'my_videos' && false){ var page = parseInt(area || '1') || 1; myVideos.fetchStream(page, '', function(){ updateHeight('#my_videos'); }); return true; } if(tab == 'related_sites' && areas && matchPosition(areas)){ var seconds = parsePosition(areas); scrollRelated(seconds); return false; } if(matchPosition(area) || matchAction(area)){ parts.unshift('1'); area = parts[0]; } if(tab == 'expand' && area && area.match(/\d+/)) { var num = parseInt(area); if(num < 100){ //FIX ME. 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vp.playFromPlaylist(pls[pls.length-1]); vp.playVideo(); scrollToPlaylistPosition(vp); }); return true; } } if(playQueue){ playQueueUpdate(); vp.playVideo(); parsed = true; playShouldStart = 0; } } if(previewMode){ var vids = []; var dur = 0; var pl = vp.getActualPlaylist(); area = parts[0]; if(parts.length == 1 && matchPosition(parts[0])){ vids = parseDash('1-'+pl.length); dur = parsePosition(parts[0]); parts = []; }else if(parts.length == 1 && matchDash(parts[0])){ vids = parseDash(parts[0]); dur = parsePosition("999:59"); parts = []; } if(parts.length == 2 && matchDash(parts[0]) && matchPosition(parts[1])){ vids = parseDash(parts[0]); dur = parsePosition(parts[1]); parts = []; } for(var i = 0; i < vids.length; i++){ playQueue.push({ 'video': pl[vids[i]-1], 'start': 0, 'stop': dur }) } if(playQueue){ playQueueUpdate(); vp.playVideo(); parsed = true; } } if(parts.length>1){ for(var i = 0; i < parts.length; i++){ var sel = findMatchingVideo(vp, parts[i]); if(sel){ playQueue.push({ 'video': sel, 'start': 0, 'stop': null }) } } if(playQueue){ playQueueUpdate(); 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if(window.history && history.replaceState && document.location.hostname.match(/^(youtube\.)?(\w{2,3}\.)?wn\.com$/)){ if(path == main_tab || path == main_tab+'/' || path == '' || path == '/') { path = basepath; } else if( path.match('^'+main_tab+'/') ){ path = basepath + '/' + path.replace(main_tab+'/', '').replace('--','/'); } else { path = basepath + '/' + path.replace('--','/'); } if(document.location.search){ path += document.location.search; } if(window.lastHistory) { history.pushState(null, null, path); } else if(window.lastHistory != path){ history.replaceState(null, null, path); window.lastHistory = path; } } else{ path = path.replace('--','/'); if(path == main_tab || path == main_tab+'/' || path == '' || path == '/') { path = ''; } if(window.lastHistory != '/'+path){ window.location.hash = path? 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Bayes' theorem

In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on conditions that might be related to the event. For example, suppose one is interested in whether a woman has cancer, and knows that she is 65. If cancer is related to age, information about her age can be used to more accurately assess the probability of her having cancer using Bayes' Theorem.

When applied, the probabilities involved in Bayes' theorem may have different probability interpretations. In one of these interpretations, the theorem is used directly as part of a particular approach to statistical inference. With the Bayesian probability interpretation the theorem expresses how a subjective degree of belief should rationally change to account for evidence: this is Bayesian inference, which is fundamental to Bayesian statistics. However, Bayes' theorem has applications in a wide range of calculations involving probabilities, not just in Bayesian inference.

Bayes theorem (disambiguation)

Bayes theorem may refer to:

Theorem

  • Bayes' theorem - a theorem which expresses how a subjective degree of belief should rationally change to account for evidence.
  • The application of the theorem

  • Bayesian theory in E-discovery - the application of Bayes' theorem in legal evidence diagnostics and E-discovery, where it provides a way of updating the probability of an event in the light of new information.
  • Bayesian theory in marketing - the application of Bayes' theorem in marketing, where it allows for decision making and market research evaluation under uncertainty and limited data.
  • Podcasts:

    • Bayes' Theorem - The Simplest Case

      ►Second Bayes' Theorem example: https://www.youtube.com/watch?v=k6Dw0on6NtM ►Third Bayes' Theorem example: https://www.youtube.com/watch?v=HaYbxQC61pw ►FULL Discrete Math Playlist: https://www.youtube.com/watch?v=rdXw7Ps9vxc&list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS Bayes' Theorem is an incredibly powerful theorem in probability that allows us to relate P(A|B) to P(B|A). This is helpful because we often have an asymmetry where one of these conditional probabilities is easy to compute and the other is not. It let's us treat compute how to update our probabilities given new information. The formula: P(A|B) = P(B|A)P(A)/P(B) 0:00 Deriving Bayes' Theorem 1:40 The Formula 2:57 First Example Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation...

      published: 19 Nov 2017
    • Bayes theorem, the geometry of changing beliefs

      Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.com The quick proof: https://youtu.be/U_85TaXbeIo Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/ The study with Steve: https://science.sciencemag.org/content/185/4157/1124 http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project. Contents: 0:00 - Intro example 4:09 - Generalizing as a formula 10:13 - Making probabilit...

      published: 22 Dec 2019
    • Bayes' Theorem of Probability With Tree Diagrams & Venn Diagrams

      This video tutorial provides an intro into Bayes' Theorem of probability. It explains how to use the formula in solving example problems in addition to using tree diagrams and venn diagrams. Probability - Free Formula Sheet: https://bit.ly/3zb22rW _______________________________ Introduction to Probability: https://www.youtube.com/watch?v=SkidyDQuupA Probability Formulas: https://www.youtube.com/watch?v=bddckR734aM Probability Explained: https://www.youtube.com/watch?v=UORztmWGY6Q Probability With Geometry: https://www.youtube.com/watch?v=DeH5aHWxEaI Probability of Complementary Events: https://www.yout...

      published: 04 Apr 2019
    • Bayes' Theorem, Clearly Explained!!!!

      Bayes' Theorem is the foundation of Bayesian Statistics. This video was you through, step-by-step, how it is easily derived and why it is useful. For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large a...

      published: 16 Aug 2021
    • Bayes' Theorem EXPLAINED with Examples

      Learn how to solve any Bayes' Theorem problem. This tutorial first explains the concept behind Bayes' Theorem, where the equation comes from, and finally how to use the formula in an example. Bayes' Theorem is one of the most common equations covered in Statistics due to its numerous applications to the real world. It is also one of the most misunderstood theorems, but this video will help clear all of that up! For more help, visit: https://theacetutors.com For more videos/content, visit: https://theacetutors.com/blog Sign up for tutoring: https://theacetutors.com/register

      published: 04 Apr 2023
    • The Bayesian Trap

      Bayes' theorem explained with examples and implications for life. Check out Audible: http://ve42.co/audible Support Veritasium on Patreon: http://ve42.co/patreon I didn't say it explicitly in the video, but in my view the Bayesian trap is interpreting events that happen repeatedly as events that happen inevitably. They may be inevitable OR they may simply be the outcome of a series of steps, which likely depend on our behaviour. Yet our expectation of a certain outcome often leads us to behave just as we always have which only ensures that outcome. To escape the Bayesian trap, we must be willing to experiment. Special thanks to Patreon supporters: Tony Fadell, Jeff Straathof, Donal Botkin, Zach Mueller, Ron Neal, Nathan Hansen, Saeed Alghamdi Useful references: The Signal and the Noise,...

      published: 05 Apr 2017
    • The quick proof of Bayes' theorem

      Including some added words on independence. Main video: https://youtu.be/HZGCoVF3YvM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spoti...

      published: 22 Dec 2019
    • Intro to Bayes’s Theorem | Probability Theory

      What is Bayes’s theorem for conditional probability? We'll be proving it briefly in today's lesson, as it is a direct result of the definition of conditional probabilities. We'll also see how Baye's theorem works with a sample space partitioned into separate events, and an example of applying Baye's theorem! Baye's theorem gives us a way to calculate the conditional probability P(A|B) using P(B|A). We know that the probability of A given B, P(A|B), is equal to P(A and B)/P(B) and P(B|A) = P(B and A)/P(A) = P(A and B)/P(A). Then, multiplying both sides of the second equation by P(A) we have that P(B|A)*P(A) = P(A and B) and we can substitute this into our expression for P(A|B). Thus, we have P(A|B) = P(B|A)P(A)/P(B), and this is Baye's theorem (sometimes called Baye's rule). Often times, ...

      published: 19 Aug 2020
    • How to systematically approach truth - Bayes' rule

      The philosopher Gottfried Wilhelm Leibniz had a dream. He hoped that progress in philosophy and mathematics would eventually yield a method to systematically figure out the truth. This video explores an approach to that dream that takes us some of the way there: Bayesianism. The basic idea of Bayesianism is to represent beliefs as probabilities and update them using the formal rules of probability theory to the best of our ability. In particular, Bayes' rule tells us how to update our degree of belief in a hypothesis after observing some evidence. Bayes' rule can inform many central tenets of scientific reasoning. One example is Cromwell's rule, which tells us with the language of probability theory that our empirical beliefs shouldn't be absolute dogmas, but always potentially put into qu...

      published: 19 Feb 2022
    • Everything You Ever Wanted to Know About Bayes' Theorem But Were Afraid To Ask.

      Probability has an improbable history. Thomas Bayes deserves credit for introducing conditional probability but The Frequentists didn’t make it easy. Wizard of Odds explores the slippery side of probability and the powerful role it plays in modern life. This program features Robert C. Green, Leonard Mlodinow, Masoud Mohseni, and Alan Peters. Original program date: Saturday, May 30, 2015 Watch the full program here: https://youtu.be/92A5iDjxgOg Visit our Website: http://www.worldsciencefestival.com/ Like us on Facebook: https://www.facebook.com/worldsciencefestival Instagram: @worldscifest Follow us on twitter: https://twitter.com/WorldSciFest

      published: 27 Oct 2015
    developed with YouTube
    Bayes' Theorem - The Simplest Case
    5:31

    Bayes' Theorem - The Simplest Case

    • Order:
    • Duration: 5:31
    • Uploaded Date: 19 Nov 2017
    • views: 1558657
    ►Second Bayes' Theorem example: https://www.youtube.com/watch?v=k6Dw0on6NtM ►Third Bayes' Theorem example: https://www.youtube.com/watch?v=HaYbxQC61pw ►FULL Discrete Math Playlist: https://www.youtube.com/watch?v=rdXw7Ps9vxc&list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS Bayes' Theorem is an incredibly powerful theorem in probability that allows us to relate P(A|B) to P(B|A). This is helpful because we often have an asymmetry where one of these conditional probabilities is easy to compute and the other is not. It let's us treat compute how to update our probabilities given new information. The formula: P(A|B) = P(B|A)P(A)/P(B) 0:00 Deriving Bayes' Theorem 1:40 The Formula 2:57 First Example Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor OTHER COURSE PLAYLISTS: ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography
    https://wn.com/Bayes'_Theorem_The_Simplest_Case
    Bayes theorem, the geometry of changing beliefs
    15:11

    Bayes theorem, the geometry of changing beliefs

    • Order:
    • Duration: 15:11
    • Uploaded Date: 22 Dec 2019
    • views: 4555622
    Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.com The quick proof: https://youtu.be/U_85TaXbeIo Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/ The study with Steve: https://science.sciencemag.org/content/185/4157/1124 http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project. Contents: 0:00 - Intro example 4:09 - Generalizing as a formula 10:13 - Making probability intuitive 13:35 - Issues with the Steve example Thanks to these viewers for their contributions to translations Gujarati: Hitesh12358, Pragna1991 Hebrew: Omer Tuchfeld Italian: @crampaldo ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
    https://wn.com/Bayes_Theorem,_The_Geometry_Of_Changing_Beliefs
    Bayes' Theorem of Probability With Tree Diagrams & Venn Diagrams
    19:14

    Bayes' Theorem of Probability With Tree Diagrams & Venn Diagrams

    • Order:
    • Duration: 19:14
    • Uploaded Date: 04 Apr 2019
    • views: 1044335
    This video tutorial provides an intro into Bayes' Theorem of probability. It explains how to use the formula in solving example problems in addition to using tree diagrams and venn diagrams. Probability - Free Formula Sheet: https://bit.ly/3zb22rW _______________________________ Introduction to Probability: https://www.youtube.com/watch?v=SkidyDQuupA Probability Formulas: https://www.youtube.com/watch?v=bddckR734aM Probability Explained: https://www.youtube.com/watch?v=UORztmWGY6Q Probability With Geometry: https://www.youtube.com/watch?v=DeH5aHWxEaI Probability of Complementary Events: https://www.youtube.com/watch?v=0T-CaQCiSf4 Conditional Probability: https://www.youtube.com/watch?v=sqDVrXq_eh0 __________________________________ Independent and Dependent Events: https://www.youtube.com/watch?v=lWAdPyvm400 Probability of Mutual Exclusive Events: https://www.youtube.com/watch?v=X6usGgwXFyU Multiplication and Addition Rule: https://www.youtube.com/watch?v=94AmzeR9n2w Compound Probability: https://www.youtube.com/watch?v=EHU6pVSczb4 Expected Value: https://www.youtube.com/watch?v=b6VK2VPMXNI Probability Tree Diagrams: https://www.youtube.com/watch?v=w4wKXVwtGac ___________________________________ Bayes Theorem: https://www.youtube.com/watch?v=OByl4RJxnKA Probability - Binomial Distribution: https://www.youtube.com/watch?v=3PWKQiLK41M Probability - Geometric Distribution: https://www.youtube.com/watch?v=d5iAWPnrH6w Probability - Poisson Distribution: https://www.youtube.com/watch?v=m0o-585xwW0 Continuous Probability Distributions: https://www.youtube.com/watch?v=QxqxdQ_g2uw Probability Density Functions: https://www.youtube.com/watch?v=3xAIWiTJCvE __________________________________ Probability - Uniform Distributions: https://www.youtube.com/watch?v=KfunVw-0AH0 Probability - Exponential Distributions: https://www.youtube.com/watch?v=J3KSjZFVbis Probability - Normal Distributions (Calculus): https://www.youtube.com/watch?v=gHBL5Zau3NE Probability - Standard Normal Distributions: https://www.youtube.com/watch?v=CjF_yQ2N638 Probability - The Law of Large Numbers: https://www.youtube.com/watch?v=ihTpK6dXSas ___________________________________ Final Exams and Video Playlists: https://www.video-tutor.net/ Full-Length Videos and Worksheets: https://www.patreon.com/MathScienceTutor/collections
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    Bayes' Theorem, Clearly Explained!!!!
    14:00

    Bayes' Theorem, Clearly Explained!!!!

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    • Uploaded Date: 16 Aug 2021
    • views: 368534
    Bayes' Theorem is the foundation of Bayesian Statistics. This video was you through, step-by-step, how it is easily derived and why it is useful. For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 3:05 A note about notation 5:21 Deriving Bayes' Theorem 9:12 Why Bayes' Theorem is useful 11:39 Another note about notation #StatQuest #Probability #Bayesian
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    Bayes' Theorem EXPLAINED with Examples
    8:03

    Bayes' Theorem EXPLAINED with Examples

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    • Uploaded Date: 04 Apr 2023
    • views: 305344
    Learn how to solve any Bayes' Theorem problem. This tutorial first explains the concept behind Bayes' Theorem, where the equation comes from, and finally how to use the formula in an example. Bayes' Theorem is one of the most common equations covered in Statistics due to its numerous applications to the real world. It is also one of the most misunderstood theorems, but this video will help clear all of that up! For more help, visit: https://theacetutors.com For more videos/content, visit: https://theacetutors.com/blog Sign up for tutoring: https://theacetutors.com/register
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    The Bayesian Trap
    10:37

    The Bayesian Trap

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    • Duration: 10:37
    • Uploaded Date: 05 Apr 2017
    • views: 4176503
    Bayes' theorem explained with examples and implications for life. Check out Audible: http://ve42.co/audible Support Veritasium on Patreon: http://ve42.co/patreon I didn't say it explicitly in the video, but in my view the Bayesian trap is interpreting events that happen repeatedly as events that happen inevitably. They may be inevitable OR they may simply be the outcome of a series of steps, which likely depend on our behaviour. Yet our expectation of a certain outcome often leads us to behave just as we always have which only ensures that outcome. To escape the Bayesian trap, we must be willing to experiment. Special thanks to Patreon supporters: Tony Fadell, Jeff Straathof, Donal Botkin, Zach Mueller, Ron Neal, Nathan Hansen, Saeed Alghamdi Useful references: The Signal and the Noise, Nate Silver The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy, by Sharon Bertsch McGrayne Bayes' theorem or rule (there are many different versions of the same concept) has fascinated me for a long time due to its uses both in mathematics and statistics, and to solve real world problems. Bayesian inference has been used to crack the Enigma Code and to filter spam email. Bayes has also been used to locate the wreckage from plane crashes deep beneath the sea. Music from http://epidemicsound.com "Flourishing Views 3"
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    The quick proof of Bayes' theorem
    3:48

    The quick proof of Bayes' theorem

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    • Uploaded Date: 22 Dec 2019
    • views: 497620
    Including some added words on independence. Main video: https://youtu.be/HZGCoVF3YvM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
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    Intro to Bayes’s Theorem | Probability Theory
    12:41

    Intro to Bayes’s Theorem | Probability Theory

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    • Duration: 12:41
    • Uploaded Date: 19 Aug 2020
    • views: 56358
    What is Bayes’s theorem for conditional probability? We'll be proving it briefly in today's lesson, as it is a direct result of the definition of conditional probabilities. We'll also see how Baye's theorem works with a sample space partitioned into separate events, and an example of applying Baye's theorem! Baye's theorem gives us a way to calculate the conditional probability P(A|B) using P(B|A). We know that the probability of A given B, P(A|B), is equal to P(A and B)/P(B) and P(B|A) = P(B and A)/P(A) = P(A and B)/P(A). Then, multiplying both sides of the second equation by P(A) we have that P(B|A)*P(A) = P(A and B) and we can substitute this into our expression for P(A|B). Thus, we have P(A|B) = P(B|A)P(A)/P(B), and this is Baye's theorem (sometimes called Baye's rule). Often times, we will have to calculate P(B) in the denominator using the Law of Total Probability. I meant to put this in the video as a caption: the example problem is from "Probability" by Jim Pitman. Intro to Conditional Probability: https://www.youtube.com/watch?v=FtFR80FcJjU Law of Total Probability: https://www.youtube.com/watch?v=U3_783xznQI ◆ Donate on PayPal: https://www.paypal.me/wrathofmath ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons I hope you find this video helpful, and be sure to ask any questions down in the comments! ******************************************************************** The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work. Vallow Bandcamp: https://vallow.bandcamp.com/ Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW Vallow SoundCloud: https://soundcloud.com/benwatts-3 ******************************************************************** +WRATH OF MATH+ Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Music Channel: http://www.youtube.com/seanemusic
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    How to systematically approach truth - Bayes' rule
    19:08

    How to systematically approach truth - Bayes' rule

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    • Uploaded Date: 19 Feb 2022
    • views: 115567
    The philosopher Gottfried Wilhelm Leibniz had a dream. He hoped that progress in philosophy and mathematics would eventually yield a method to systematically figure out the truth. This video explores an approach to that dream that takes us some of the way there: Bayesianism. The basic idea of Bayesianism is to represent beliefs as probabilities and update them using the formal rules of probability theory to the best of our ability. In particular, Bayes' rule tells us how to update our degree of belief in a hypothesis after observing some evidence. Bayes' rule can inform many central tenets of scientific reasoning. One example is Cromwell's rule, which tells us with the language of probability theory that our empirical beliefs shouldn't be absolute dogmas, but always potentially put into question when new evidence comes in. ERRATA: - At 8:37, there should be P(H|e) on the left-hand side. ▀▀▀▀▀▀▀▀▀PATREON, MEMBERSHIP, KO-FI▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 🟠 Patreon: https://www.patreon.com/rationalanimations 🟢Merch: https://crowdmade.com/collections/rational-animations 🔵 Channel membership: https://www.youtube.com/channel/UCgqt1RE0k0MIr0LoyJRy2lg/join 🟤 Ko-fi, for one-time and recurring donations: https://ko-fi.com/rationalanimations ▀▀▀▀▀▀▀▀▀SOCIAL & DISCORD▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Twitter: https://twitter.com/RationalAnimat1 Discord: https://discord.gg/hxWBm6sBNU ▀▀▀▀▀▀▀▀▀LINKS & READINGS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Arbital's guide to Bayes' rule: https://arbital.com/p/bayes_rule/?l=1zq The bayesian view of scientific virtues: https://arbital.com/p/bayes_science_virtues/ @3blue1brown 's explanations: 1. https://youtu.be/HZGCoVF3YvM 2. https://youtu.be/U_85TaXbeIo 3. https://youtu.be/lG4VkPoG3ko 4. https://youtu.be/ZA4JkHKZM50 5. https://youtu.be/8idr1WZ1A7Q @measureofdoubt's explanation of bayesian thinking: https://youtu.be/BrK7X_XlGB8 Two beautiful books containing many essays on bayesian thinking and truth-seeking: 1. Map and Territory, by Eliezer Yudkowsky: https://www.amazon.com/Map-Territory-Rationality-AI-Zombies/dp/1939311233/ref=sr_1_2?crid=2EFD6G3N09W7Y&keywords=eliezer&qid=1645017447&sprefix=elieze%2Caps%2C156&sr=8-2 2. How to Actually Change Your Mind, by Eliezer Yudkowsky: https://www.amazon.com/Actually-Change-Your-Mind-Rationality/dp/1939311276/ref=sr_1_5?crid=2EFD6G3N09W7Y&keywords=eliezer&qid=1645017447&sprefix=elieze%2Caps%2C156&sr=8-5 Probability Theory, The Logic of Science, by E.T.Jaynes. This is THE book on bayesian thinking applied to science (more advanced): https://www.amazon.com/Probability-Theory-Science-T-Jaynes/dp/0521592712/ref=sr_1_1?crid=3263961XQEYON&keywords=jaynes+probability+theory&qid=1645017539&sprefix=jaynes+probability+theory%2Caps%2C135&sr=8-1 ▀▀▀▀▀▀▀▀▀OTHER STUFF▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Share this video with a friend or on Social Media: https://youtu.be/4hHA-oqpNig Playlist with all the animated videos: https://www.youtube.com/watch?v=GgyX-MnRAuY&list=PL1Nr7ps7wyYo-0AOYd6lfKp-6Czh4p5On Bitcoin address: 1FX4iepZfh1yuMNYtvYf2CWL7gha8cakuf Ethereum address: 0xDa8463494Dd233c3aBe59bc42Abc4D50823A5f3 ▀▀▀▀▀▀▀▀▀PATRONS & MEMBERS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ BIG thanks to our patrons & members from the simple adder tier and above: Lexi X רם רינגל Ana Tomasovic Ashten The Platypus Bryan Egan Calvin McCarter Chris Chapin Craig Ludington Dan Wahl David Mc Florian Gabriel Ledung hr101 Jacob Van Buren Jeroen De Dauw JHeb John S Lars Osborne Logic Luke Freeman Meade Marmalade Nathan Nathan Fish Nicholas Kees Dupuis Nick Sharp noggieB Raphaël Lévy Roborodger Sephiths Superslowmojoe Tim Duffy Udo Austin Cluff Connor Dang Griffith FusionOak Mark Gongloff Matthew Brooks Neel Nanda rictic Robin Hanson Ryouta Takehiko Scott Alexander YouAyePee Bleys Goodson Dawson Francisco Lillo marverati Matt Parlmer Michael Zimmermann no special person Trevyn Case William Deng Gabriel Fair Thomas Farago ▀▀▀▀▀▀▀CREDITS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Script by: - Matthew Barnett - The guy with the weird accent Animation by: - :3 Narration by Robert Miles: https://www.youtube.com/c/RobertMilesAI ▀▀▀▀▀▀▀MUSIC▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Brandenburg Concerto No4-1 BWV1049 - Classical Whimsical by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/ Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100303 Artist: http://incompetech.com/ ▀▀▀▀▀▀▀CHAPTERS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Chapters: 0:00 - Mathematicizing truth-seeking 1:55 - Conditional probability 3:39 - Explanation of Bayes' rule 10:34 - The odds form 14:54 - Cromwell's rule 17:36 - The bayesian view of truth-seeking
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    Everything You Ever Wanted to Know About Bayes' Theorem But Were Afraid To Ask.
    5:48

    Everything You Ever Wanted to Know About Bayes' Theorem But Were Afraid To Ask.

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    • Uploaded Date: 27 Oct 2015
    • views: 76746
    Probability has an improbable history. Thomas Bayes deserves credit for introducing conditional probability but The Frequentists didn’t make it easy. Wizard of Odds explores the slippery side of probability and the powerful role it plays in modern life. This program features Robert C. Green, Leonard Mlodinow, Masoud Mohseni, and Alan Peters. Original program date: Saturday, May 30, 2015 Watch the full program here: https://youtu.be/92A5iDjxgOg Visit our Website: http://www.worldsciencefestival.com/ Like us on Facebook: https://www.facebook.com/worldsciencefestival Instagram: @worldscifest Follow us on twitter: https://twitter.com/WorldSciFest
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    Bayes' Theorem - The Simplest Case

    ►Second Bayes' Theorem example: https://www.youtube.com/watch?v=k6Dw0on6NtM ►Third Bayes' Theorem example: https://www.youtube.com/watch?v=HaYbxQC61pw ►FULL Discrete Math Playlist: https://www.youtube.com/watch?v=rdXw7Ps9vxc&list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS Bayes' Theorem is an incredibly powerful theorem in probability that allows us to relate P(A|B) to P(B|A). This is helpful because we often have an asymmetry where one of these conditional probabilities is easy to compute and the other is not. It let's us treat compute how to update our probabilities given new information. The formula: P(A|B) = P(B|A)P(A)/P(B) 0:00 Deriving Bayes' Theorem 1:40 The Formula 2:57 First Example Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor OTHER COURSE PLAYLISTS: ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography
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    ►Second Bayes' Theorem example: https://www.youtube.com/watch?v=k6Dw0on6NtM ►Third Bayes' ...
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    Bayes theorem, the geometry of changing beliefs
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    The Bayesian Trap
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    The quick proof of Bayes' theorem
    Including some added words on independence. Main video: https://youtu.be/HZGCoVF3YvM Help ...
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    Intro to Bayes’s Theorem | Probability Theory
    What is Bayes’s theorem for conditional probability? We'll be proving it briefly in today'...
    published: 19 Aug 2020
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    Bayes' theorem

    In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on conditions that might be related to the event. For example, suppose one is interested in whether a woman has cancer, and knows that she is 65. If cancer is related to age, information about her age can be used to more accurately assess the probability of her having cancer using Bayes' Theorem.

    When applied, the probabilities involved in Bayes' theorem may have different probability interpretations. In one of these interpretations, the theorem is used directly as part of a particular approach to statistical inference. With the Bayesian probability interpretation the theorem expresses how a subjective degree of belief should rationally change to account for evidence: this is Bayesian inference, which is fundamental to Bayesian statistics. However, Bayes' theorem has applications in a wide range of calculations involving probabilities, not just in Bayesian inference.

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